Solve -2/3x^2+4/3+2=0

$$- \frac{ 2 }{ 3 } { x }^{ 2 } + \frac{ 4 }{ 3 } +2=0$$

Solve for x

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

Steps by Finding Square Root

Add \frac{4}{3} and 2 to get \frac{10}{3}.

$$-\frac{2}{3}x^{2}+\frac{10}{3}=0$$

Subtract \frac{10}{3} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{2}{3}x^{2}=-\frac{10}{3}$$

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}.

$$x^{2}=-\frac{10}{3}\left(-\frac{3}{2}\right)$$

Multiply -\frac{10}{3} and -\frac{3}{2} to get 5.

$$x^{2}=5$$

Take the square root of both sides of the equation.

$$x=\sqrt{5} x=-\sqrt{5}$$

Steps Using the Quadratic Formula

Add \frac{4}{3} and 2 to get \frac{10}{3}.

$$-\frac{2}{3}x^{2}+\frac{10}{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{2}{3} for a, 0 for b, and \frac{10}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{2}{3}\right)\times \frac{10}{3}}}{2\left(-\frac{2}{3}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{2}{3}\right)\times \frac{10}{3}}}{2\left(-\frac{2}{3}\right)}$$

Multiply -4 times -\frac{2}{3}.

$$x=\frac{0±\sqrt{\frac{8}{3}\times \frac{10}{3}}}{2\left(-\frac{2}{3}\right)}$$

Multiply \frac{8}{3} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{\frac{80}{9}}}{2\left(-\frac{2}{3}\right)}$$

Take the square root of \frac{80}{9}.

$$x=\frac{0±\frac{4\sqrt{5}}{3}}{2\left(-\frac{2}{3}\right)}$$

Multiply 2 times -\frac{2}{3}.

$$x=\frac{0±\frac{4\sqrt{5}}{3}}{-\frac{4}{3}}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{5}}{3}}{-\frac{4}{3}} when ± is plus.

$$x=-\sqrt{5}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{5}}{3}}{-\frac{4}{3}} when ± is minus.

$$x=\sqrt{5}$$

The equation is now solved.

$$x=-\sqrt{5} x=\sqrt{5}$$